Families of Varieties of General Type

Inbunden, Engelska, 2023

Del 231 i serien Cambridge Tracts in Mathematics

1 784 kr

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Beskrivning

This book establishes the moduli theory of stable varieties, giving the optimal approach to understanding families of varieties of general type. Starting from the Deligne-Mumford theory of the moduli of curves and using Mori's program as a main tool, the book develops the techniques necessary for a theory in all dimensions. The main results give all the expected general properties, including a projective coarse moduli space. A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.

Produktinformation

Utgivningsdatum:2023-04-20
Mått:159 x 235 x 34 mm
Vikt:880 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Tracts in Mathematics
Antal sidor:490
Förlag:Cambridge University Press
ISBN:9781009346108

Utforska kategorier

Talteori inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

János Kollár is Professor of Mathematics at Princeton University. He has received the Cole Prize (2006), the Nemmers Prize (2016), and the Shaw Prize (2017). He is the author of more than 200 articles and ten books, mostly on algebraic geometry.

Recensioner i media

'This book dismantles the final, most daunting barriers to learning about moduli of higher dimensional varieties, from the point of view of the Minimal Model Program. The first chapter draws the reader in with a compelling history; a discussion of the main ideas; a visitor's trail through the subject, complete with guardrails around the most dangerous traps; and a rundown of the issues that one must overcome. The text that follows is the outcome of Kollár's monumental three-decades-long effort, with the final stones laid just in the last few years.' Dan Abramovich, Brown University

Innehållsförteckning

Introduction; Notation; 1. History of moduli problems; 2. One-parameter families; 3. Families of stable varieties; 4. Stable pairs over reduced base schemes; 5. Numerical flatness and stability criteria; 6. Moduli problems with flat divisorial part; 7. Cayley flatness; 8. Moduli of stable pairs; 9. Hulls and husks; 10. Ancillary results; 11. Minimal models and their singularities; References; Index.